Problem: Simplify the following expression: $q = \dfrac{8}{3a - 6} \div \dfrac{2}{2a}$
Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{8}{3a - 6} \times \dfrac{2a}{2}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 8 \times 2a } { (3a - 6) \times 2}$ $q = \dfrac{16a}{6a - 12}$ Simplify: $q = \dfrac{8a}{3a - 6}$